Performance prediction for Natural Language Processing (NLP) seeks to reduce the experimental burden resulting from the myriad of different evaluation scenarios, e.g., the combination of languages used in multilingual transfer. In this work, we explore the framework ofBayesian matrix factorisation for performance prediction, as many experimental settings in NLP can be naturally represented in matrix format. Our approach outperforms the state-of-the-art in several NLP benchmarks, including machine translation and cross-lingual entity linking. Furthermore, it also avoids hyperparameter tuning and is able to provide uncertainty estimates over predictions.